TP Informatique 18 - Calcul approché d`intégrales 1 1 Méthode des

f[a, b]Zb
a
f(t)dt
ε
lim
n→+∞=Zb
a
f(t)dt
lim
n→+∞=Zb
a
f(t)dt
f[a, b]
Rn=
|f0|6M[a, b],
Zb
a
f(t)dt −Rn 6M
n(b−a)2
Z1
0
e−t2dt
10−4Z1
0
e−t2
f:x7→ e−x2∀x>0,|f0(x)|6r2
e
Mn=
|f00|6K[a, b]
Zb
a
f(t)dt −Mn 6K
24
(b−a)3
n2
10−5Z2
1
e−t
√t
f:x7→ e−t
√t∀x>1,|f00(x)|611
4e

f[a, b]Zb
a
f(t)dt
x=a x =bCf
n
p
p
n
1
√πZn
0
e−t2dt n
1000 ×n
1
√πZ+∞
0
e−t2dt = lim
n→+∞
1
√πZn
0
e−t2dt